Ebook: Dynamical Systems a Differential Geometric Approach to Symmetry and Reduction

In their discussion of the subject of classical mechanics, the authors of this book use a new and stimulating approach which involves looking at dynamical systems from the viewpoint of differential geometry. They discuss the reduction of these systems, and the role played by symmetry and invariance in such reductions. Central to their approach is the view that symmetry is a tool to be applied to a model system after it has been built or discovered, rather than forming the foundation of such a system. The book is divided into two parts. The first is introductory, dealing with the foundations of mechanics, and describing the construction of a model system from the data available. The second part concentrates on invariance, symmetry and reduction; significantly, it discusses the importance of understanding local (Lie Algebra) and global (Lie Group) symmetry within the framework of the reduction of dynamical systems. 'Digressions' throughout the text explain the mathematical principles behind the concepts described.